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                    第2章 线程管理
            
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                    2.1 线程的基本操作
            
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                    2.2 传递参数
            
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                    2.3 转移所有权
            
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                    2.4 确定线程数量
            
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                    2.5 线程标识
            
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                    2.6 本章总结
            
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                    第3章 共享数据
            
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                    3.1 共享数据的问题
            
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                    3.2 使用互斥量
            
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                    3.3 保护共享数据的方式
            
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                    3.4 本章总结
            
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                    第4章 同步操作
            
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                    4.1 等待事件或条件
            
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                    4.2 使用future
            
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                    4.3 限时等待
            
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                    4.4 简化代码
            
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                    4.5 本章总结
            
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                    第5章 内存模型和原子操作
            
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                    5.1 内存模型
            
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                    5.2 原子操作和原子类型
            
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                    5.3 同步操作和强制排序
            
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                    5.4 本章总结
            
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                    第6章 设计基于锁的并发数据结构
            
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                    6.1 并发设计的意义
            
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                    6.2 基于锁的并发数据结构
            
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                    6.3 设计更加复杂的数据结构
            
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                    6.4 本章总结
            
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                    第7章 设计无锁的并发数据结构
            
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                    7.1 定义和意义
            
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                    7.2 无锁数据结构的例子
            
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                    7.3 设计无锁数据结构的指导建议
            
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                    7.4 本章总结
            
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        <li class="chapter " data-level="1.15" data-path="../chapter8/8.0-chinese.html">
            
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                    第8章 并发设计
            
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                    8.1 线程间划分工作
            
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                    8.2 并发代码的性能
            
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                    8.3 为多线程性能设计数据结构
            
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                    8.4 设计并发代码的注意事项
            
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                    8.5 在实践中设计并发代码
            
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                    8.6 本章总结
            
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                    第9章 高级线程管理
            
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                    9.1 线程池
            
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                    9.2 中断线程
            
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                    9.3 本章总结
            
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        <li class="chapter " data-level="1.17" data-path="../chapter10/10.0-chinese.html">
            
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                    第10章 并行算法
            
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        <li class="chapter " data-level="1.17.1" data-path="../chapter10/10.1-chinese.html">
            
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                    10.1 并行化标准库算法
            
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        <li class="chapter " data-level="1.17.2" data-path="../chapter10/10.2-chinese.html">
            
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                    10.2 执行策略
            
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        <li class="chapter " data-level="1.17.3" data-path="../chapter10/10.3-chinese.html">
            
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                    10.3 C++标准库中的并行算法
            
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                    10.4 本章总结
            
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                    第11章 测试和调试多线程应用
            
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        <li class="chapter " data-level="1.18.1" data-path="../chapter11/11.1-chinese.html">
            
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                    11.1 与并发相关的Bug
            
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        <li class="chapter " data-level="1.18.2" data-path="../chapter11/11.2-chinese.html">
            
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                    11.2 定位并发Bug的技巧
            
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        <li class="chapter " data-level="1.18.3" data-path="../chapter11/11.3-chinese.html">
            
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                    11.3 本章总结
            
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        <li class="chapter " data-level="1.19" data-path="../appendix_A/A.0-chinese.html">
            
                <a href="../appendix_A/A.0-chinese.html">
            
                    
                    附录A C++11特性简明参考(部分)
            
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        <li class="chapter " data-level="1.19.1" data-path="../appendix_A/A.1-chinese.html">
            
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                    A.1 右值引用
            
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        <li class="chapter " data-level="1.19.2" data-path="../appendix_A/A.2-chinese.html">
            
                <a href="../appendix_A/A.2-chinese.html">
            
                    
                    A.2 删除函数
            
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        <li class="chapter " data-level="1.19.3" data-path="../appendix_A/A.3-chinese.html">
            
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                    A.3 默认函数
            
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        <li class="chapter " data-level="1.19.4" data-path="../appendix_A/A.4-chinese.html">
            
                <a href="../appendix_A/A.4-chinese.html">
            
                    
                    A.4 常量表达式函数
            
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        <li class="chapter " data-level="1.19.5" data-path="../appendix_A/A.5-chinese.html">
            
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                    A.5 Lambda函数
            
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        <li class="chapter " data-level="1.19.6" data-path="../appendix_A/A.6-chinese.html">
            
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                    A.6 变参模板
            
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        <li class="chapter " data-level="1.19.7" data-path="../appendix_A/A.7-chinese.html">
            
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                    A.7 自动推导变量类型
            
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        <li class="chapter " data-level="1.19.8" data-path="../appendix_A/A.8-chinese.html">
            
                <a href="../appendix_A/A.8-chinese.html">
            
                    
                    A.8 线程本地变量
            
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        <li class="chapter " data-level="1.19.9" data-path="../appendix_A/A.9-chinese.html">
            
                <a href="../appendix_A/A.9-chinese.html">
            
                    
                    A.9 模板类参数的推导
            
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        <li class="chapter " data-level="1.19.10" data-path="../appendix_A/A.10-chinese.html">
            
                <a href="../appendix_A/A.10-chinese.html">
            
                    
                    A.10 本章总结
            
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                                <h1 id="d6-ratio&#x5934;&#x6587;&#x4EF6;">D.6 &lt;ratio&gt;&#x5934;&#x6587;&#x4EF6;</h1>
<p><code>&lt;ratio&gt;</code>&#x5934;&#x6587;&#x4EF6;&#x63D0;&#x4F9B;&#x5728;&#x7F16;&#x8BD1;&#x65F6;&#x8FDB;&#x884C;&#x7684;&#x8BA1;&#x7B97;&#x3002;</p>
<p><strong>&#x5934;&#x6587;&#x4EF6;&#x5185;&#x5BB9;</strong></p>
<pre><code>namespace std
{
  template&lt;intmax_t N,intmax_t D=1&gt;
  class ratio;

  // ratio arithmetic
  template &lt;class R1, class R2&gt;
  using ratio_add = see description;

  template &lt;class R1, class R2&gt;
  using ratio_subtract = see description;

  template &lt;class R1, class R2&gt;
  using ratio_multiply = see description;

  template &lt;class R1, class R2&gt;
  using ratio_divide = see description;

  // ratio comparison
  template &lt;class R1, class R2&gt;
  struct ratio_equal;

  template &lt;class R1, class R2&gt;
  struct ratio_not_equal;

  template &lt;class R1, class R2&gt;
  struct ratio_less;

  template &lt;class R1, class R2&gt;
  struct ratio_less_equal;

  template &lt;class R1, class R2&gt;
  struct ratio_greater;

  template &lt;class R1, class R2&gt;
  struct ratio_greater_equal;

  typedef ratio&lt;1, 1000000000000000000&gt; atto;
  typedef ratio&lt;1, 1000000000000000&gt; femto;
  typedef ratio&lt;1, 1000000000000&gt; pico;
  typedef ratio&lt;1, 1000000000&gt; nano;
  typedef ratio&lt;1, 1000000&gt; micro;
  typedef ratio&lt;1, 1000&gt; milli;
  typedef ratio&lt;1, 100&gt; centi;
  typedef ratio&lt;1, 10&gt; deci;
  typedef ratio&lt;10, 1&gt; deca;
  typedef ratio&lt;100, 1&gt; hecto;
  typedef ratio&lt;1000, 1&gt; kilo;
  typedef ratio&lt;1000000, 1&gt; mega;
  typedef ratio&lt;1000000000, 1&gt; giga;
  typedef ratio&lt;1000000000000, 1&gt; tera;
  typedef ratio&lt;1000000000000000, 1&gt; peta;
  typedef ratio&lt;1000000000000000000, 1&gt; exa;
}
</code></pre><h2 id="d61-stdratio&#x7C7B;&#x578B;&#x6A21;&#x677F;">D.6.1 std::ratio&#x7C7B;&#x578B;&#x6A21;&#x677F;</h2>
<p><code>std::ratio</code>&#x7C7B;&#x578B;&#x6A21;&#x677F;&#x63D0;&#x4F9B;&#x4E86;&#x4E00;&#x79CD;&#x5BF9;&#x5728;&#x7F16;&#x8BD1;&#x65F6;&#x8FDB;&#x884C;&#x8BA1;&#x7B97;&#x7684;&#x673A;&#x5236;&#xFF0C;&#x901A;&#x8FC7;&#x8C03;&#x7528;&#x5408;&#x7406;&#x7684;&#x6570;&#xFF0C;&#x4F8B;&#x5982;&#xFF1A;&#x534A;(<code>std::ratio&lt;1,2&gt;</code>),2/3(std::ratio<2, 3="">)&#x6216;15/43(std::ratio<15, 43="">)&#x3002;&#x5176;&#x4F7F;&#x7528;&#x5728;C++&#x6807;&#x51C6;&#x5E93;&#x5185;&#x90E8;&#xFF0C;&#x7528;&#x4E8E;&#x521D;&#x59CB;&#x5316;<code>std::chrono::duration</code>&#x7C7B;&#x578B;&#x6A21;&#x677F;&#x3002;</15,></2,></p>
<p><strong>&#x7C7B;&#x578B;&#x5B9A;&#x4E49;</strong></p>
<pre><code>template &lt;intmax_t N, intmax_t D = 1&gt;
class ratio
{
public:
  typedef ratio&lt;num, den&gt; type;
  static constexpr intmax_t num= see below;
  static constexpr intmax_t den= see below;
};
</code></pre><p><strong>&#x8981;&#x6C42;</strong>
D&#x4E0D;&#x80FD;&#x4E3A;0&#x3002;</p>
<p><strong>&#x63CF;&#x8FF0;</strong>
num&#x548C;den&#x5206;&#x522B;&#x4E3A;&#x5206;&#x5B50;&#x548C;&#x5206;&#x6BCD;&#xFF0C;&#x6784;&#x9020;&#x5206;&#x6570;N/D&#x3002;den&#x603B;&#x662F;&#x6B63;&#x6570;&#x3002;&#x5F53;N&#x548C;D&#x7684;&#x7B26;&#x53F7;&#x76F8;&#x540C;&#xFF0C;&#x90A3;&#x4E48;num&#x4E3A;&#x6B63;&#x6570;&#xFF1B;&#x5426;&#x5219;num&#x4E3A;&#x8D1F;&#x6570;&#x3002;</p>
<p><strong>&#x4F8B;&#x5B50;</strong></p>
<pre><code>ratio&lt;4,6&gt;::num == 2
ratio&lt;4,6&gt;::den == 3
ratio&lt;4,-6&gt;::num == -2
ratio&lt;4,-6&gt;::den == 3
</code></pre><h2 id="d62-stdratioadd&#x6A21;&#x677F;&#x522B;&#x540D;">D.6.2 std::ratio_add&#x6A21;&#x677F;&#x522B;&#x540D;</h2>
<p><code>std::ratio_add</code>&#x6A21;&#x677F;&#x522B;&#x540D;&#x63D0;&#x4F9B;&#x4E86;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x5728;&#x7F16;&#x8BD1;&#x65F6;&#x76F8;&#x52A0;&#x7684;&#x673A;&#x5236;(&#x4F7F;&#x7528;&#x6709;&#x7406;&#x8BA1;&#x7B97;)&#x3002;</p>
<p><strong>&#x5B9A;&#x4E49;</strong></p>
<pre><code>template &lt;class R1, class R2&gt;
using ratio_add = std::ratio&lt;see below&gt;;
</code></pre><p><strong>&#x5148;&#x51B3;&#x6761;&#x4EF6;</strong>
R1&#x548C;R2&#x5FC5;&#x987B;&#x4F7F;&#x7528;<code>std::ratio</code>&#x8FDB;&#x884C;&#x521D;&#x59CB;&#x5316;&#x3002;</p>
<p><strong>&#x6548;&#x679C;</strong>
ratio_add<r1, r2="">&#x88AB;&#x5B9A;&#x4E49;&#x4E3A;&#x4E00;&#x4E2A;&#x522B;&#x540D;&#xFF0C;&#x5982;&#x679C;&#x4E24;&#x6570;&#x53EF;&#x4EE5;&#x8BA1;&#x7B97;&#xFF0C;&#x4E14;&#x65E0;&#x6EA2;&#x51FA;&#xFF0C;&#x8BE5;&#x7C7B;&#x578B;&#x53EF;&#x4EE5;&#x8868;&#x793A;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x5BF9;&#x8C61;R1&#x548C;R2&#x7684;&#x548C;&#x3002;&#x5982;&#x679C;&#x8BA1;&#x7B97;&#x51FA;&#x6765;&#x7684;&#x7ED3;&#x679C;&#x6EA2;&#x51FA;&#x4E86;&#xFF0C;&#x90A3;&#x4E48;&#x7A0B;&#x5E8F;&#x91CC;&#x9762;&#x5C31;&#x6709;&#x95EE;&#x9898;&#x4E86;&#x3002;&#x5728;&#x7B97;&#x672F;&#x6EA2;&#x51FA;&#x7684;&#x60C5;&#x51B5;&#x4E0B;&#xFF0C;<code>std::ratio_add&lt;R1, R2&gt;</code>&#x5E94;&#x8BE5;&#x5E94;&#x8BE5;&#x4E0E;<code>std::ratio&lt;R1::num * R2::den + R2::num * R1::den, R1::den * R2::den&gt;</code>&#x76F8;&#x540C;&#x3002;</r1,></p>
<p><strong>&#x4F8B;&#x5B50;</strong></p>
<pre><code>std::ratio_add&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;2,5&gt; &gt;::num == 11
std::ratio_add&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;2,5&gt; &gt;::den == 15

std::ratio_add&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;7,6&gt; &gt;::num == 3
std::ratio_add&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;7,6&gt; &gt;::den == 2
</code></pre><h2 id="d63-stdratiosubtract&#x6A21;&#x677F;&#x522B;&#x540D;">D.6.3 std::ratio_subtract&#x6A21;&#x677F;&#x522B;&#x540D;</h2>
<p><code>std::ratio_subtract</code>&#x6A21;&#x677F;&#x522B;&#x540D;&#x63D0;&#x4F9B;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x6570;&#x5728;&#x7F16;&#x8BD1;&#x65F6;&#x8FDB;&#x884C;&#x76F8;&#x51CF;(&#x4F7F;&#x7528;&#x6709;&#x7406;&#x8BA1;&#x7B97;)&#x3002;</p>
<p><strong>&#x5B9A;&#x4E49;</strong></p>
<pre><code>template &lt;class R1, class R2&gt;
using ratio_subtract = std::ratio&lt;see below&gt;;
</code></pre><p><strong>&#x5148;&#x51B3;&#x6761;&#x4EF6;</strong>
R1&#x548C;R2&#x5FC5;&#x987B;&#x4F7F;&#x7528;<code>std::ratio</code>&#x8FDB;&#x884C;&#x521D;&#x59CB;&#x5316;&#x3002;</p>
<p><strong>&#x6548;&#x679C;</strong>
ratio_add<r1, r2="">&#x88AB;&#x5B9A;&#x4E49;&#x4E3A;&#x4E00;&#x4E2A;&#x522B;&#x540D;&#xFF0C;&#x5982;&#x679C;&#x4E24;&#x6570;&#x53EF;&#x4EE5;&#x8BA1;&#x7B97;&#xFF0C;&#x4E14;&#x65E0;&#x6EA2;&#x51FA;&#xFF0C;&#x8BE5;&#x7C7B;&#x578B;&#x53EF;&#x4EE5;&#x8868;&#x793A;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x5BF9;&#x8C61;R1&#x548C;R2&#x7684;&#x548C;&#x3002;&#x5982;&#x679C;&#x8BA1;&#x7B97;&#x51FA;&#x6765;&#x7684;&#x7ED3;&#x679C;&#x6EA2;&#x51FA;&#x4E86;&#xFF0C;&#x90A3;&#x4E48;&#x7A0B;&#x5E8F;&#x91CC;&#x9762;&#x5C31;&#x6709;&#x95EE;&#x9898;&#x4E86;&#x3002;&#x5728;&#x7B97;&#x672F;&#x6EA2;&#x51FA;&#x7684;&#x60C5;&#x51B5;&#x4E0B;&#xFF0C;<code>std::ratio_subtract&lt;R1, R2&gt;</code>&#x5E94;&#x8BE5;&#x5E94;&#x8BE5;&#x4E0E;<code>std::ratio&lt;R1::num * R2::den - R2::num * R1::den, R1::den * R2::den&gt;</code>&#x76F8;&#x540C;&#x3002;</r1,></p>
<p><strong>&#x4F8B;&#x5B50;</strong></p>
<pre><code>std::ratio_subtract&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;1,5&gt; &gt;::num == 2
std::ratio_subtract&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;1,5&gt; &gt;::den == 15

std::ratio_subtract&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;7,6&gt; &gt;::num == -5
std::ratio_subtract&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;7,6&gt; &gt;::den == 6
</code></pre><h2 id="d64-stdratiomultiply&#x6A21;&#x677F;&#x522B;&#x540D;">D.6.4 std::ratio_multiply&#x6A21;&#x677F;&#x522B;&#x540D;</h2>
<p><code>std::ratio_multiply</code>&#x6A21;&#x677F;&#x522B;&#x540D;&#x63D0;&#x4F9B;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x6570;&#x5728;&#x7F16;&#x8BD1;&#x65F6;&#x8FDB;&#x884C;&#x76F8;&#x4E58;(&#x4F7F;&#x7528;&#x6709;&#x7406;&#x8BA1;&#x7B97;)&#x3002;</p>
<p><strong>&#x5B9A;&#x4E49;</strong></p>
<pre><code>template &lt;class R1, class R2&gt;
using ratio_multiply = std::ratio&lt;see below&gt;;
</code></pre><p><strong>&#x5148;&#x51B3;&#x6761;&#x4EF6;</strong>
R1&#x548C;R2&#x5FC5;&#x987B;&#x4F7F;&#x7528;<code>std::ratio</code>&#x8FDB;&#x884C;&#x521D;&#x59CB;&#x5316;&#x3002;</p>
<p><strong>&#x6548;&#x679C;</strong>
ratio_add<r1, r2="">&#x88AB;&#x5B9A;&#x4E49;&#x4E3A;&#x4E00;&#x4E2A;&#x522B;&#x540D;&#xFF0C;&#x5982;&#x679C;&#x4E24;&#x6570;&#x53EF;&#x4EE5;&#x8BA1;&#x7B97;&#xFF0C;&#x4E14;&#x65E0;&#x6EA2;&#x51FA;&#xFF0C;&#x8BE5;&#x7C7B;&#x578B;&#x53EF;&#x4EE5;&#x8868;&#x793A;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x5BF9;&#x8C61;R1&#x548C;R2&#x7684;&#x548C;&#x3002;&#x5982;&#x679C;&#x8BA1;&#x7B97;&#x51FA;&#x6765;&#x7684;&#x7ED3;&#x679C;&#x6EA2;&#x51FA;&#x4E86;&#xFF0C;&#x90A3;&#x4E48;&#x7A0B;&#x5E8F;&#x91CC;&#x9762;&#x5C31;&#x6709;&#x95EE;&#x9898;&#x4E86;&#x3002;&#x5728;&#x7B97;&#x672F;&#x6EA2;&#x51FA;&#x7684;&#x60C5;&#x51B5;&#x4E0B;&#xFF0C;<code>std::ratio_multiply&lt;R1, R2&gt;</code>&#x5E94;&#x8BE5;&#x5E94;&#x8BE5;&#x4E0E;<code>std::ratio&lt;R1::num * R2::num, R1::den * R2::den&gt;</code>&#x76F8;&#x540C;&#x3002;</r1,></p>
<p><strong>&#x4F8B;&#x5B50;</strong></p>
<pre><code>std::ratio_multiply&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;2,5&gt; &gt;::num == 2
std::ratio_multiply&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;2,5&gt; &gt;::den == 15

std::ratio_multiply&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;15,7&gt; &gt;::num == 5
std::ratio_multiply&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;15,7&gt; &gt;::den == 7
</code></pre><h2 id="d65-stdratiodivide&#x6A21;&#x677F;&#x522B;&#x540D;">D.6.5 std::ratio_divide&#x6A21;&#x677F;&#x522B;&#x540D;</h2>
<p><code>std::ratio_divide</code>&#x6A21;&#x677F;&#x522B;&#x540D;&#x63D0;&#x4F9B;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x6570;&#x5728;&#x7F16;&#x8BD1;&#x65F6;&#x8FDB;&#x884C;&#x76F8;&#x9664;(&#x4F7F;&#x7528;&#x6709;&#x7406;&#x8BA1;&#x7B97;)&#x3002;</p>
<p><strong>&#x5B9A;&#x4E49;</strong></p>
<pre><code>template &lt;class R1, class R2&gt;
using ratio_multiply = std::ratio&lt;see below&gt;;
</code></pre><p><strong>&#x5148;&#x51B3;&#x6761;&#x4EF6;</strong>
R1&#x548C;R2&#x5FC5;&#x987B;&#x4F7F;&#x7528;<code>std::ratio</code>&#x8FDB;&#x884C;&#x521D;&#x59CB;&#x5316;&#x3002;</p>
<p><strong>&#x6548;&#x679C;</strong>
ratio_add<r1, r2="">&#x88AB;&#x5B9A;&#x4E49;&#x4E3A;&#x4E00;&#x4E2A;&#x522B;&#x540D;&#xFF0C;&#x5982;&#x679C;&#x4E24;&#x6570;&#x53EF;&#x4EE5;&#x8BA1;&#x7B97;&#xFF0C;&#x4E14;&#x65E0;&#x6EA2;&#x51FA;&#xFF0C;&#x8BE5;&#x7C7B;&#x578B;&#x53EF;&#x4EE5;&#x8868;&#x793A;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x5BF9;&#x8C61;R1&#x548C;R2&#x7684;&#x548C;&#x3002;&#x5982;&#x679C;&#x8BA1;&#x7B97;&#x51FA;&#x6765;&#x7684;&#x7ED3;&#x679C;&#x6EA2;&#x51FA;&#x4E86;&#xFF0C;&#x90A3;&#x4E48;&#x7A0B;&#x5E8F;&#x91CC;&#x9762;&#x5C31;&#x6709;&#x95EE;&#x9898;&#x4E86;&#x3002;&#x5728;&#x7B97;&#x672F;&#x6EA2;&#x51FA;&#x7684;&#x60C5;&#x51B5;&#x4E0B;&#xFF0C;<code>std::ratio_multiply&lt;R1, R2&gt;</code>&#x5E94;&#x8BE5;&#x5E94;&#x8BE5;&#x4E0E;<code>std::ratio&lt;R1::num * R2::num * R2::den, R1::den * R2::den&gt;</code>&#x76F8;&#x540C;&#x3002;</r1,></p>
<p><strong>&#x4F8B;&#x5B50;</strong></p>
<pre><code>std::ratio_divide&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;2,5&gt; &gt;::num == 5
std::ratio_divide&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;2,5&gt; &gt;::den == 6

std::ratio_divide&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;15,7&gt; &gt;::num == 7
std::ratio_divide&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;15,7&gt; &gt;::den == 45
</code></pre><h2 id="d66-stdratioequal&#x7C7B;&#x578B;&#x6A21;&#x677F;">D.6.6 std::ratio_equal&#x7C7B;&#x578B;&#x6A21;&#x677F;</h2>
<p><code>std::ratio_equal</code>&#x7C7B;&#x578B;&#x6A21;&#x677F;&#x63D0;&#x4F9B;&#x5728;&#x7F16;&#x8BD1;&#x65F6;&#x6BD4;&#x8F83;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x6570;(&#x4F7F;&#x7528;&#x6709;&#x7406;&#x8BA1;&#x7B97;)&#x3002;</p>
<p><strong>&#x7C7B;&#x578B;&#x5B9A;&#x4E49;</strong></p>
<pre><code>template &lt;class R1, class R2&gt;
class ratio_equal:
  public std::integral_constant&lt;
    bool,(R1::num == R2::num) &amp;&amp; (R1::den == R2::den)&gt;
{};
</code></pre><p><strong>&#x5148;&#x51B3;&#x6761;&#x4EF6;</strong>
R1&#x548C;R2&#x5FC5;&#x987B;&#x4F7F;&#x7528;<code>std::ratio</code>&#x8FDB;&#x884C;&#x521D;&#x59CB;&#x5316;&#x3002;</p>
<p><strong>&#x4F8B;&#x5B50;</strong></p>
<pre><code>std::ratio_equal&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;2,6&gt; &gt;::value == true
std::ratio_equal&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;1,6&gt; &gt;::value == false
std::ratio_equal&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;2,3&gt; &gt;::value == false
std::ratio_equal&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;1,3&gt; &gt;::value == true
</code></pre><h2 id="d67-stdrationotequal&#x7C7B;&#x578B;&#x6A21;&#x677F;">D.6.7 std::ratio_not_equal&#x7C7B;&#x578B;&#x6A21;&#x677F;</h2>
<p><code>std::ratio_not_equal</code>&#x7C7B;&#x578B;&#x6A21;&#x677F;&#x63D0;&#x4F9B;&#x5728;&#x7F16;&#x8BD1;&#x65F6;&#x6BD4;&#x8F83;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x6570;(&#x4F7F;&#x7528;&#x6709;&#x7406;&#x8BA1;&#x7B97;)&#x3002;</p>
<p><strong>&#x7C7B;&#x578B;&#x5B9A;&#x4E49;</strong></p>
<pre><code>template &lt;class R1, class R2&gt;
class ratio_not_equal:
  public std::integral_constant&lt;bool,!ratio_equal&lt;R1,R2&gt;::value&gt;
{};
</code></pre><p><strong>&#x5148;&#x51B3;&#x6761;&#x4EF6;</strong>
R1&#x548C;R2&#x5FC5;&#x987B;&#x4F7F;&#x7528;<code>std::ratio</code>&#x8FDB;&#x884C;&#x521D;&#x59CB;&#x5316;&#x3002;</p>
<p><strong>&#x4F8B;&#x5B50;</strong></p>
<pre><code>std::ratio_not_equal&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;2,6&gt; &gt;::value == false
std::ratio_not_equal&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;1,6&gt; &gt;::value == true
std::ratio_not_equal&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;2,3&gt; &gt;::value == true
std::ratio_not_equal&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;1,3&gt; &gt;::value == false
</code></pre><h2 id="d68-stdratioless&#x7C7B;&#x578B;&#x6A21;&#x677F;">D.6.8 std::ratio_less&#x7C7B;&#x578B;&#x6A21;&#x677F;</h2>
<p><code>std::ratio_less</code>&#x7C7B;&#x578B;&#x6A21;&#x677F;&#x63D0;&#x4F9B;&#x5728;&#x7F16;&#x8BD1;&#x65F6;&#x6BD4;&#x8F83;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x6570;(&#x4F7F;&#x7528;&#x6709;&#x7406;&#x8BA1;&#x7B97;)&#x3002;</p>
<p><strong>&#x7C7B;&#x578B;&#x5B9A;&#x4E49;</strong></p>
<pre><code>template &lt;class R1, class R2&gt;
class ratio_less:
  public std::integral_constant&lt;bool,see below&gt;
{};
</code></pre><p><strong>&#x5148;&#x51B3;&#x6761;&#x4EF6;</strong>
R1&#x548C;R2&#x5FC5;&#x987B;&#x4F7F;&#x7528;<code>std::ratio</code>&#x8FDB;&#x884C;&#x521D;&#x59CB;&#x5316;&#x3002;</p>
<p><strong>&#x6548;&#x679C;</strong>
std::ratio_less<r1,r2>&#x53EF;&#x901A;&#x8FC7;<code>std::integral_constant&lt;bool, value &gt;</code>&#x5BFC;&#x51FA;&#xFF0C;&#x8FD9;&#x91CC;value&#x4E3A;<code>(R1::num*R2::den) &lt; (R2::num*R1::den)</code>&#x3002;&#x5982;&#x679C;&#x6709;&#x53EF;&#x80FD;&#xFF0C;&#x9700;&#x8981;&#x5B9E;&#x73B0;&#x4F7F;&#x7528;&#x4E00;&#x79CD;&#x673A;&#x5236;&#x6765;&#x907F;&#x514D;&#x8BA1;&#x7B97;&#x7ED3;&#x679C;&#x5DF2;&#x51FA;&#x3002;&#x5F53;&#x6EA2;&#x51FA;&#x53D1;&#x751F;&#xFF0C;&#x90A3;&#x4E48;&#x7A0B;&#x5E8F;&#x4E2D;&#x5C31;&#x80AF;&#x5B9A;&#x6709;&#x9519;&#x8BEF;&#x3002;</r1,r2></p>
<p><strong>&#x4F8B;&#x5B50;</strong></p>
<pre><code>std::ratio_less&lt;std::ratio&lt;1,3&gt;, std::ratio&lt;2,6&gt; &gt;::value == false
std::ratio_less&lt;std::ratio&lt;1,6&gt;, std::ratio&lt;1,3&gt; &gt;::value == true
std::ratio_less&lt;
  std::ratio&lt;999999999,1000000000&gt;,
  std::ratio&lt;1000000001,1000000000&gt; &gt;::value == true
std::ratio_less&lt;
  std::ratio&lt;1000000001,1000000000&gt;,
  std::ratio&lt;999999999,1000000000&gt; &gt;::value == false
</code></pre><h2 id="d69-stdratiogreater&#x7C7B;&#x578B;&#x6A21;&#x677F;">D.6.9 std::ratio_greater&#x7C7B;&#x578B;&#x6A21;&#x677F;</h2>
<p><code>std::ratio_greater</code>&#x7C7B;&#x578B;&#x6A21;&#x677F;&#x63D0;&#x4F9B;&#x5728;&#x7F16;&#x8BD1;&#x65F6;&#x6BD4;&#x8F83;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x6570;(&#x4F7F;&#x7528;&#x6709;&#x7406;&#x8BA1;&#x7B97;)&#x3002;</p>
<p><strong>&#x7C7B;&#x578B;&#x5B9A;&#x4E49;</strong></p>
<pre><code>template &lt;class R1, class R2&gt;
class ratio_greater:
  public std::integral_constant&lt;bool,ratio_less&lt;R2,R1&gt;::value&gt;
{};
</code></pre><p><strong>&#x5148;&#x51B3;&#x6761;&#x4EF6;</strong>
R1&#x548C;R2&#x5FC5;&#x987B;&#x4F7F;&#x7528;<code>std::ratio</code>&#x8FDB;&#x884C;&#x521D;&#x59CB;&#x5316;&#x3002;</p>
<h2 id="d610-stdratiolessequal&#x7C7B;&#x578B;&#x6A21;&#x677F;">D.6.10 std::ratio_less_equal&#x7C7B;&#x578B;&#x6A21;&#x677F;</h2>
<p><code>std::ratio_less_equal</code>&#x7C7B;&#x578B;&#x6A21;&#x677F;&#x63D0;&#x4F9B;&#x5728;&#x7F16;&#x8BD1;&#x65F6;&#x6BD4;&#x8F83;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x6570;(&#x4F7F;&#x7528;&#x6709;&#x7406;&#x8BA1;&#x7B97;)&#x3002;</p>
<p><strong>&#x7C7B;&#x578B;&#x5B9A;&#x4E49;</strong></p>
<pre><code>template &lt;class R1, class R2&gt;
class ratio_less_equal:
  public std::integral_constant&lt;bool,!ratio_less&lt;R2,R1&gt;::value&gt;
{};
</code></pre><p><strong>&#x5148;&#x51B3;&#x6761;&#x4EF6;</strong>
R1&#x548C;R2&#x5FC5;&#x987B;&#x4F7F;&#x7528;<code>std::ratio</code>&#x8FDB;&#x884C;&#x521D;&#x59CB;&#x5316;&#x3002;</p>
<h2 id="d611-stdratiogreaterequal&#x7C7B;&#x578B;&#x6A21;&#x677F;">D.6.11 std::ratio_greater_equal&#x7C7B;&#x578B;&#x6A21;&#x677F;</h2>
<p><code>std::ratio_greater_equal</code>&#x7C7B;&#x578B;&#x6A21;&#x677F;&#x63D0;&#x4F9B;&#x5728;&#x7F16;&#x8BD1;&#x65F6;&#x6BD4;&#x8F83;&#x4E24;&#x4E2A;<code>std::ratio</code>&#x6570;(&#x4F7F;&#x7528;&#x6709;&#x7406;&#x8BA1;&#x7B97;)&#x3002;</p>
<p><strong>&#x7C7B;&#x578B;&#x5B9A;&#x4E49;</strong></p>
<pre><code>template &lt;class R1, class R2&gt;
class ratio_greater_equal:
  public std::integral_constant&lt;bool,!ratio_less&lt;R1,R2&gt;::value&gt;
{};
</code></pre><p><strong>&#x5148;&#x51B3;&#x6761;&#x4EF6;</strong>
R1&#x548C;R2&#x5FC5;&#x987B;&#x4F7F;&#x7528;<code>std::ratio</code>&#x8FDB;&#x884C;&#x521D;&#x59CB;&#x5316;&#x3002;</p>

                                
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